Evaluation Questions | Set Theory

1. Given µ = {1, 2, 3, ….., 10}, N= {even numbers},

F = {numbers divisible by 5}

G = {numbers greater than 3}.

i. Write down the following statements using symbols 5 and 10 are both greater than 3.

ii. If a is a number such that a ϵ N,  a ϵ F,  a ϵ µ  and a ϵ G, what is a?

iii. If b is a number such that b ϵ N and b ∈ G, what is the value of b?

iv. Draw a Venn diagram showing , N, F and G

2. Assuming that x is an integer, state the lowest and the highest values of x for each of the following ranges:

i. -8 ≤ x ≤ 9         

ii. 2 ≤ x < 10         

iii. -8 < x < -1           

iv. \( \scriptsize -5 \frac{2}{3} \) < x < \( \scriptsize 1 \frac{3}{4} \)

3. In a village all the people speak Hausa or English or both. If 97% speak Hausa and 64% speak English, what percentage speak both languages?

4. In a class of 35 students, 19 take History and 12 take Economics. If 5 take both subjects, how many take neither?

5. Out of 25 teachers, 16 are married and 15 are women. If 6 of the men are married, how many of the women are not married?

6. A school sports team contains 68 students. 33 do field events, 40 do track events. If 15 students do field event only and 10 do both swimming and track events, how many students do:

i. Swimming only

ii. track events only

iii. all three events?

7. 110 members of a Sports Club play at least one of the games, football, basketball, and volleyball only, 15 play football and volleyball only, 26play basketball and volleyball only, x play all the three games, 2x each play only one game, how many play basketball altogether?